Denote by \((q,p)\)  the coordinates on \(\Lambda \) . Assuming \(\Lambda \)  is a \(C^r\)  submanifold of \(M\) , and the spectral gap is of size \(r\)  we can introduce, as in [1]}, \(C^{r-1}\)  coordinates \((s,u,q,p)\)  in a neighbourhood \(U_0\)  of \(\Lambda \) , where \(s,u\)  belong to a neighbourhood of the origin in \(\mathbb {R}^m\)  such that:
